Solving policy design problems: Alternating direction method of multipliers-based methods for structured inverse variational inequalities
Solving policy design problems: Alternating direction method of multipliers-based methods for structured inverse variational inequalities
复制标题
解决政策设计问题：结构化逆变分不等式的基于乘子的方法的交替方向法
DOI：
10.1016/j.ejor.2019.05.044
复制
发表时间：
2020
影响因子：
6.4
通讯作者：
Deren Han
中科院分区：
文献类型：
--
作者：
Yaning Jiang;Xingju Cai;Deren Han
逆变分不等式在各个学科中有着广泛的应用，其中一些变分不等式具有非常吸引人的结构。有几种算法（例如，近似点算法和投影型算法），但很少有人充分利用了这一特殊结构。本文考虑了一类具有可分结构和线性约束的逆变分不等式，它的根源是空间经济均衡问题。为了设计一个有效的算法，我们开发了一个交替方向的乘法器（ADMM）的方法，利用可分离的结构。在适当的假设下，证明了算法的全局收敛性.我们提出了一个改进的变体，使子问题更容易，并得出在相同的条件下的收敛结果。最后，我们提出了初步的数值结果显示所提出的方法的能力和效率。
Inverse variational inequalities have broad applications in various disciplines, and some of them have very appealing structures. There are several algorithms (e.g., proximal point algorithms and projection-type algorithms) for solving the inverse variational inequalities in general settings, while few of them have fully exploited the special structures. In this paper, we consider a class of inverse variational inequalities that has a separable structure and linear constraints, which has its root in spatial economic equilibrium problems. To design an efficient algorithm, we develop an alternating direction method of multipliers (ADMM) based method by utilizing the separable structure. Under some mild assumptions, we prove its global convergence. We propose an improved variant that makes the subproblems much easier and derive the convergence result under the same conditions. Finally, we present the preliminary numerical results to show the capability and efficiency of the proposed methods.